An observer is stationary on a merry-go-round at a distance \(R=3 \mathrm{~m}\) from the axis of rotation. The merry-go-round, starting from a standstill, begins to rotate with constant angular acceleration \(\dot{\omega}=0.1 \mathrm{rad} / \mathrm{s}^{2}\). Determine the time \(t_{1}\) at which the merry-go-round reaches the angular velocity of 0.1 revolutions per second and the magnitude of the observer's felt acceleration at time \(t_{1}\).